Research On Cross Efficiency Of Data Envelopment Analysis(DEA):Theoretical Method And Application

In reality, the evaluation and selection of the decision making units (DMUs) are the common and important work. In order to evaluate DMUs, many evaluation methods have been proposed by experts and scholars. Among these methods, Data Envelopment Analysis (DEA) has been generally accepted by scholars and researchers, which could evaluate efficiencies of a set of homogenous DMUs with multiple inputs and multiple outputs. The significant characteristic of DEA is that it does not require any preliminary parameter estimation and functional relation assumptions between inputs and outputs, which avoids bias caused by human factors. Because of this advantage, DEA method has been rapidly developed and widely used. However, traditional DEA models only classify all DMUs into efficient and inefficient DMUs, and those efficient DMUs cannot be differentiated any further. In addition, these traditional models usually generate the case that the weights at very small values (or even zero) are assigned to some inputs or outputs and very large values to other inputs or outputs. This may lead to that the efficiency of DMU under evaluation is overestimated. In order to solve these problems, cross-efficiency evaluation based on DEA has been proposed, which evaluates efficiencies of DMUs through self-and peer-evaluations. This method has two main advantages. On one hand, cross-efficiency evaluation has a strong discrimination power and usually provides a full ranking for all evaluated DMUs. On the other hand, unrealistic weight results could be avoided without requiring any weight restrictions. However, there are still some defects in cross-efficiency evaluation. Firstly, the optimal weights calculated by the traditional DEA model are generally not unique, which lead to non-uniqueness of cross-efficiency scores. This has reduced the usefulness of cross-efficiency evaluation. Secondly, averaging the cross-efficiency will lose the association between weights and results, thus it will not provide information for decision makers to improve the performance of DMUs. Lastly, the existing cross-efficiency methods pay little attention to case that some specific DMUs may have a cooperative relationship while some form of competition may exist among other DMUs. To overcome these drawbacks, this paper introduces multiple attribute decision making theory and game theory into DEA for proposing new cross-efficiency approaches. The main researches of the paper are as follows.Chapter1firstly summarizes the fundamental theory of DEA, and then comprehensively reviews the existing research results related to this thesis. These research results include the evaluation methods based on DEA, cross-efficiency evaluation methods and the main allocation methods of emission permits. Finally, the research contents and structure of this paper are provided.Chapter2studies on the non-uniqueness of cross-efficiency evaluation. This chapter firstly discusses the problem of non-uniqueness when cross-efficiency evaluation is used to evaluate the DMUs, and points out the disadvantages of the existing improved approaches. Then two different secondary models are proposed. Each model could not only effectively deal with the problem of non-uniqueness, but also reduce the differences between the weighted inputs or weighted outputs during the evaluation process. Thus all inputs and outputs in these newly proposed models can be fully used as much as possible.Chapter3proposes two different cross-efficiency aggregation methods from the perspective of multiple attribute decision making to eliminate the assumption of average. The new methods not only keep theories consist with classical cross-efficiency method, but also evaluate and rank DMUs from different angles. In addition, this chapter also proposes interval cross-efficiency evaluation and aggregation methods to evaluate the efficiencies of DMUs with interval data. The validity of each proposed method is examined by the empirical example.Chapter4firstly points out that traditional cross-efficiency methods consider the DMUs only have competitive or cooperative relationships. In reality, some specific DMUs may have a cooperative relationship, and some form of direct or indirect competition may exist among other DMUs. However, the existing DEA models cannot deal with this case. To address the need to simultaneously consider competition and cooperation, two cross-efficiency methods are proposed through comprehensively consider the defects of existing game cross-efficiency methods. Two empirical examples are illustrated to examine the validity of the proposed method.Chapter5studies the allocation of emission permits using DEA. This chapter proposed several models from the perspectives of centralization and coordination of individual rationality to research initial allocation and reallocation of emission permits. Compared with the traditional allocation methods, the proposed DEA models consider the input and output levels simultaneously, and could provide the reasonable allocation results. A paper mill example is illustrated to examine the validity of the proposed methods. Chapter6summarized the main research work of the thesis, and points out possible extensions for future study and improvement.